The graph shows a proportional relationship between time and the number of boxes a machine packages. How many boxes does the machine package in 5 minutes? your graph: (write down) Y axis number of boxes, 0- - 120- - 240- - 360- - 480-. X Axis Time (minutes), 0- - 2- - 4- - 6- - 8-.
Accroding to the graph.:
0 min 0 boxes
2 min 120boxes
4 min 240 boxes
6 min 360 boxes
8 min 480 boxes.
So 2 minutes "gives us" 120 boxes
120/2= 60 boxes per minute.
In 5 minutes the machine package does 5*60=300 boxes.
From the proportional relationship, machine will package 300 boxes in 5 minutes.
Given points on the graph are,
Here, x-values represent time in minutes and y-values represent the number of boxes packed.
Since, x and y show the proportional relationship,
Expression showing the relationship will be → y ∝ x
Or y = kx
Here, k is a proportionality constant.
k = \(\frac{y}{x}\)
From the points given, we choose one point (2, 120).
k = \(\frac{120}{2}\)
k = 60
Therefore, equation will be,
60 = \(\frac{y}{x}\)
y = 60x
For x = 5 minutes,
y = 60×5
y = 300 boxes
Therefore, 300 boxes the machine will package in 5 minutes.
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